This debate didn't solve this at all.
How is this played? Do you play the F and then the F, A, D together, or do you not play the first F, and then play the F, A, D together. And if you don't play the F at all, then why do you play the other quarter notes with the exact same notation, or do you not play any of the quarter notes?
You play the F, A and D at the same time. There is only one F to be played. All other quarter notes are played as they are, and are unimpacted by the "extra" F.
The reason the extra F is there is to communicate to the reader that the F in the D + A + F chord serves as part of the melody.
I see one potential point of confusion that other answers haven't covered. You ask about timing, and which notes you play first or play together. You might be asking because the F quarter note appears to the left of the other notes. This doesn't actually mean anything about timing; both the quarter and half note Fs count as "beat one"; it's just that one has to be shifted a bit to avoid overlapping.
This is about the idea of having multiple "voices" at once. This might seem odd since you're not a choir, just one pianist. But the idea is that your one instrument can "suggest" multiple ones at once, or that "if this music were being sung by a choir, here are the notes that one voice would sing."
Let's make up a simple example. Say this is the melody:
Now let's add a few notes:
The way we've notated this, with noteheads sharing a single stem, we're implying that this is not two voices, just a single instrument that can play double stops. But what if this were actually for two singers? On beat one, what happens? Do they both sing F, or does one of them rest? Both could be options:
For singers, those two versions are very different. But for piano, the two examples above will be performed almost exactly the same. You'll press the F key, then the F and A together, etc. So why bother notating it this way? Well, for one thing, even if both examples wind up sounding exactly the same, it shows an idea about the music. Notated music is more than instructions about what to press when. And secondly, you might try to show the different ideas by making some notes louder or more connected than others.
Now, say you want this:
You want to press the F key on beat one, and keep it down while adding A in beat two. This is one way to show it. But so is this:
These two notations say the same thing about timing. The only difference is that the second one shows "two voices." And honestly it might be even clearer than the previous one, in which the tie could be confused for a slur between the F and the A. In the second notation, you still only press the F key once. The quarter notehead is shifted to the left since it can't just overlap the half note, but they happen at the same time. And, as a pianist, you only have the one key to press, but if this were sung, two people would both be singing Fs at that moment.
This notates multiple voices where two voices fall together in one voice. This means you play the a and the f and keep them pressed over the next beat where you add the c. It then requires some differentiated touch to phrase this in such a way that the individual voices are audible.
Alternatively one might increase differentiation by playing certain notes early or late, but this is not specified in the score! If notated you’d expect to find tied grace notes to denote this. If it is not notated you can of course still do so as personal choice, but I see no real advantage from doing so in this particular case.
To all intents and purposes the very first F crotchet is there to 'make up the numbers'. It is the melody, and also part of the accompaniment, but the melody lasts for 1 beat, while the accompaniment lasts for two. So play F,(at the same time as the A beneath) and hold it down.
As in, this is a piano transcription, with multiple parts. The tails up could have been played by one instrument, tails down by a different one. Writing it out for piano, the sums need to add up, so the F is shown with the top line (stems up), and also middle line (of music), (tails down). So there's no need to play the F twice, just keep it pressed while you play the C after. It's a bit of a stretch, so might benefit from use of the damper pedal.
